Huerta, Schade, Granell (Eds): Connecting a Digital Europe through Location and Place. Proceedings of the AGILE'2014
International Conference on Geographic Information Science, Castellón, June, 3-6, 2014. ISBN: 978-90-816960-4-3
Qualitative Representation of Dynamic Attributes of Trajectories
Tales Paiva Nogueira
Hervé Martin
Univ. Grenoble Alpes, LIG, F-38000 Grenoble, France
CNRS, LIG, F-38000 Grenoble, France
[email protected]
[email protected]
Abstract
Trajectory dynamic characteristics may be a very relevant source of information to analyze the behaviour of moving objects. However,
most of existing works on trajectory representation deal only with basic parameters of trajectories, namely space and time. In this paper, we
show how some derivatives of the spatio-temporal dimension, e.g. speed, acceleration, direction, may be integrated in trajectory modelling.
We address the problem of representing trajectories in a way that qualitative descriptions of trajectories are stored and easily accessed
through an ontology called QualiTraj which is also flexible enough to support relevant raw data representation. We validate our proposal
with real GPS traces collected from a well-known sports tracking mobile application.
Keywords: geographical information systems, trajectory analysis, semantic trajectories, dynamic, user profile, ontologies
1
Introduction
The Internet as we know it today is constantly evolving to a
more and more connected system thanks to the increasing
quantity of data made available as linked data, building what
is called the Semantic Web [2]. With semantic web
technologies we are moving from the web of documents
towards the web of data, where machines will be able to
understand and reason about the connections among different
datasets and therefore enable the development of richer
applications. It is of common knowledge that ontologies are
well suited to represent datasets in this new paradigm.
At the same time, we are witnessing the development of
mobile technologies such as smart phones for the acquisition
of data in conjunction with many sensors as well as the grow
of technologies of geolocation (GPS, A-GPS, GLONASS)
and identification (RFID). The convergence of these
technologies allows the easy acquisition of information about
the trajectories of users using mobile devices. The acquisition,
management, modelling, and analysis of such data provide
many challenges related to the integration of these data with
systems that already exist. Therefore, it should be taken into
account that the multidimensional and multifaceted aspects of
these data potentially holds a very rich semantics. There is a
vast amount of works that propose to bridge the gap between
trajectory representation and Semantic Web technologies,
mainly regarding the representation with ontologies [1, 3, 9,
10, 13, 17, 19, 20].
The identification of mobility patterns has been an constant
topic of interest in the GIScience area in several domains like
tourism, road traffic, crisis management, marketing, etc. [8].
Several works have dealt with trajectory analysis proposing
new ways of comparing, segmenting and clustering moving
object's paths. But most of them only handle the geometric
aspect of trajectories and just a few deal with dynamic
parameters like speed and acceleration explicitly [4, 12].
In most cases, the variability of dynamic properties is very
high. Take as example the raw representation of speed of a
runner in Figure 1. Although it is obvious that the movement
did not suffer exactly the same variations as it is depicted in
the graphic due to the intrinsic error and noise of GPS
readings, we can observe that there is a need to simplify this
information so it can become more useful. The development
of new methods and tools to analyse movement components
like the one shown in Figure 1 is still a great challenge.
Figure 1: Time series of the speed profile of a runner captured
by a smart phone application without any post processing
treatment.
In this work, we argue that a qualitative representation of
trajectories components are useful and enable new queries to
be build and answer many application domain needs. The
remainder of this paper is organized as follows: in section 2,
we compare our work with similar proposals and highlight the
differences between them. In section 3, we define what are the
dynamic aspects considered in this paper. In section 4, the
AGILE 2014 – Castellón, June 3-6, 2014
QualiTraj ontology is introduced, followed by a case study in
section 5.
2
Related work
In [14], Rehrl et. al. proposed a method for semantic
processing of GPS traces where information is extracted from
raw data. Based on the assumption that the basic parameters to
express motion in space and time are velocity and course, they
defined six motion patterns with associated rules. The patterns
are the following: stand still characterizes the absence of
motion and is assumed when the velocity is less than 1 m/s;
steady motion represents the periods when there is motion
with constant velocity and is distinguished when velocity is
greater than 1 m/s and acceleration lies between −0.3 m/s² and
0.3 m/s². Positive acceleration happens when the velocity
increases and is greater than 1 m/s and acceleration is greater
than 0.3 m/s²; negative acceleration is similar but acceleration
should be less than −0.3 m/s². Positive course change is
identified when there is a course change rate above 0.4 º/s,
and negative course change is determined when this change is
below −0.4 º/s.
While this categorization has as objective to improve the
level of abstraction of motion data, the authors rely too
heavily in thresholds to characterize speed, acceleration, and
course changes. In an heterogeneous dataset, this approach
does not seem adequate as these thresholds may vary
depending on the mean of transportation. In our work, we
preferred the usage of statistic measures whenever it was
possible to avoid relying on thresholds that depends on the
nature of the data being analyzed.
In [9], van Hage et. al. presented the Simple Event Model
(SEM) and its application in the maritime domain. In their
use case, events are automatically recognized from the
Automatic Identification System (AIS) raw data and
represented as SEM instances. From that, it was possible to
characterize some types of ship behavior like slowing down,
speeding up, and anchored. Three types of data were
collected in the form of time series: location, speed, and
course. Due to the large dimensions of the tracked ships and
the fact that they do not accelerate nor change their courses
quickly, their movement are very regular and much more
easy to compress by a piecewise linear algorithm. In our
paper, instead of AIS data with speed information already
included, we have at first just GPS raw data from which we
have to calculate the speed profile. Moreover, the nature of
motion data is very different: runners instead of ships.
Runners may have a much more irregular speed,
acceleration, and changes in course direction when
compared to ships. Besides, we take a qualitative approach
towards the characterization of movement.
3
What is dynamic?
One of the most important features of spatio-temporal systems
is the ability to trace the path that a moving object follows
during some time. A trajectory can be defined as the user
defined record of the evolution of the position (perceived as a
point) of an object that is moving in space during a given time
interval in order to achieve a given goal [15]. A research topic
that is constantly studied in the trajectory analysis domain is
related to the representation of these spatio-temporal paths.
While the representation of trajectories with ontologies have
already been subject of many studies, the dynamic aspects of
trajectories are generally just mentioned as simple attributes
or even not mentioned. Most works about trajectory analysis
limits themselves to the geometric representations of
trajectories as a static curve [5].
The dynamic properties that we talk about in this paper may
have different names among the literature. Dodge et. al. [5],
for instance, call them movement parameters and separate
them in three groups: primitive parameters, primary
derivatives, and secondary derivatives. Each group is further
organized in spatial, temporal and spatio-temporal
dimensions. The primitive parameters are the ones that has
been the subject of most studies in GIS (position and time).
The primary derivatives are distance, direction, spatial extent,
duration, travel time, speed and velocity. The secondary
derivatives are spatial distribution, change of direction,
sinuosity, temporal distribution, change of duration,
acceleration, and approaching rate. In this work, we are going
to focus on the speed derivative, as we believe that this aspect
of trajectories is crucial to the characterization of the
behaviour of a moving object.
4
The QualiTraj Ontology
In this section, we present a modeling approach that enables
the representation of trajectories’ dynamic characteristics in a
high abstraction level through an ontology. Figure 2 shows the
basic structure of QualiTraj, the main contribution of this
work. The top level element is the Trajectory entity, which
represents a spatio-temporal path followed by a moving
object. Each trajectory may have one or more profiles. Each
Profile represents one dynamic aspect of a trajectory (e.g.
speed, acceleration, direction).
Profiles may have aggregated measures that might be useful
depending on the application. Thus, we included the Global
Attributes entity to store information like the average speed of
the whole trajectory.
The Segment is the entity that represents a relevant change
in the dynamic property occurred along the trajectory. This
element contains the qualitative information itself stored in
the Qualitative Value entity. Each Segment starts and ends at
a Key Point, i.e. a location in space and time that define the
bounds of the segment. The Key Points may also be used to
retrieve important information, e.g. where and when the
highest speed was achieved. While this kind of data is not
mandatory because it is application-specific and, on the
other hand, the start and end points must always be
represented, there are three relationships between Segment
and Key Point in the ontology being optional only the one
called has_point.
The kind of change is stored in the Qualitative Value entity
associated with each Segment. The application developer
should determine which values compose the lexical space of
this entity. Another important element to represent each
Segment is the Coefficient, an entity that holds the slope of the
line that connects the starting and ending points. Having this
information may be useful if we want to infer the approximate
AGILE 2014 – Castellón, June 3-6, 2014
value of the profiled characteristic using a linear equation.
The next section shows an example of the usage of the
QualiTraj ontology in a real scenario.
Figure 2: The QualiTraj ontology
data transformation steps of one short workout as it becomes
easier to spot the changes suffered by the time series through
all the steps. Figure 3 shows the raw speed data being preprocessed in order to simplify the stored data. The first graph
shows the calculated speed at each point of the trajectory
based on the latitude, longitude, and time difference between
points. We have used the Haversine formula to calculate the
approximate distance traveled during each sampled point. It is
important to notice that a good speed approximation is heavily
dependent on a good sampling rate, i.e. GPS fixes constantly
recorded in small intervals of time.
The second step of the cleaning phase consists in detecting
stops and moves of the tracked object. After that, we applied a
Kalman filter [18] in order to smooth the data and attenuate
GPS position errors. The last step of the smoothing phase is to
summary the data points with a piecewise linear segmentation
[11]. All the steps of the cleaning phase are depicted in Figure
3. In this specific example, the length of the time series was
reduced from 60 points to only 28 points without losing the
main characteristics of the signal.
Figure 3: The evolution of speed during a four-minute walk
and the steps of post-processing: (a) is the raw data, in (b)
stops and moves are identified, (c) is the filtered signal, and
(d) shows the piecewise linear segmentation result.
5
Case study
(a)
The studies about mobility analysis are numerous in the
literature. In order to validate them, it is of vital importance to
work with a representative dataset. The capture of real-life
spatio-temporal data is generally expensive and time
consuming due to the need of adequate equipment, search for
subjects willing to participate (e.g. taxi drivers, shoppers,
students), among other factors. Fortunately, there are some
available datasets that can be freely downloaded, like GeoLife
[21, 22], Reality Mining [6], geo-tagged photos from websites
like Flickr1 and Instagram2, among others.
One interesting source of trajectory data is sports tracking
websites and mobile applications, e.g. RunKeeper3,
Endomondo4, Sports Tracker5, Strava6, MapMyRun7, and
have been source of studies like the one by Ferrari and Mamei
[7]. Notwithstanding the widespread adoption of these
services by professional athletes as well as by casual
practitioners of sports activities, the collected data is not
always publicly available. The minor part of sites provide an
open API for third-party applications to access user-generated
data.
For our case study, we collected data from users of
MapMyRun application that shared their workouts publicly.
We gathered information about 10 users that logged activities
in the city of Grenoble, France, represented by 66 trajectories
in total. In order to be clearer, we are going to show the raw
1
www.flickr.com
www.instagram.com
3
www.runkeeper.com
4
www.endomondo.com
5
www.sports-tracker.com
6
www.strava.com
7
www.mapmyrun.com
2
(b)
(c)
(d)
The final step in the speed representation of this trajectory
consisted in creating the entities following the QualiTraj
model. The lexical space used for the Qualitative Value entity
was {“Increase”, “Decrease”, “Steady”, and “Stop”}. Figure 4
shows the first two Segments represented with QualiTraj. The
first segment consists in an increase of speed from 2.02 m/s to
2.40 m/s, which are the points of a line with an angle of 7.24
degrees. We omitted the timestamp and location of Key Points
to improve the readability of the example. Notice that the
AGILE 2014 – Castellón, June 3-6, 2014
same Key Point, “Key Point 2”, has been reused in both
segments, avoiding data duplication thanks to the graph
structure of the ontological modeling approach.
The authors would like to thank the French Ministry of
Higher Education and Research (Ministère de l’Enseignement
Supérieur et de la Recherche de la France – MESR) for
supporting this work.
Figure 4: Part of qualitative representation of a trajectory
using the QualiTraj ontology
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Conclusion
In this paper, we demonstrated how it is possible to enrich raw
trajectory data with dynamic aspects of movement and
provide an infrastructure for querying this new knowledge
through an ontology.
The representation of spatio-temporal data by means of
ontologies is even more useful when the inference features of
reasoners are explored. As a following activity of this work,
we will investigate how reasoners can improve the analysis of
patterns of dynamic movement parameters of trajectories.
Queries that involve more than one moving object form and
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way, more complex queries and reasoning tasks can be also
envisaged as future work.
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